3.436 \(\int \frac {e^{a+b x-c x^2}}{x} \, dx\)

Optimal. Leaf size=20 \[ \text {Int}\left (\frac {e^{a+b x-c x^2}}{x},x\right ) \]

[Out]

Unintegrable(exp(-c*x^2+b*x+a)/x,x)

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Rubi [A]  time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(a + b*x - c*x^2)/x,x]

[Out]

Defer[Int][E^(a + b*x - c*x^2)/x, x]

Rubi steps

\begin {align*} \int \frac {e^{a+b x-c x^2}}{x} \, dx &=\int \frac {e^{a+b x-c x^2}}{x} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {e^{a+b x-c x^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^(a + b*x - c*x^2)/x,x]

[Out]

Integrate[E^(a + b*x - c*x^2)/x, x]

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fricas [A]  time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (-c x^{2} + b x + a\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="fricas")

[Out]

integral(e^(-c*x^2 + b*x + a)/x, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (-c x^{2} + b x + a\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="giac")

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{-c \,x^{2}+b x +a}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-c*x^2+b*x+a)/x,x)

[Out]

int(exp(-c*x^2+b*x+a)/x,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (-c x^{2} + b x + a\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-c*x^2+b*x+a)/x,x, algorithm="maxima")

[Out]

integrate(e^(-c*x^2 + b*x + a)/x, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {e}}^{-c\,x^2+b\,x+a}}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(a + b*x - c*x^2)/x,x)

[Out]

int(exp(a + b*x - c*x^2)/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ e^{a} \int \frac {e^{b x} e^{- c x^{2}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-c*x**2+b*x+a)/x,x)

[Out]

exp(a)*Integral(exp(b*x)*exp(-c*x**2)/x, x)

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